Matrix theory over ringoids-Reference-Cited by-同舟云学术

Matrix theory over ringoids

Published:2023 Issue:30 Volume:37 Page:10275-10288
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Rezaei Akbar¹,Kim Hee²,Borzooei Rajab³,Saeid Arsham⁴

Affiliation:

1. Department of Mathematics, Payame Noor University, Tehran, Iran

2. Department of Mathematics, Hanyang University, Seoul, Korea

3. Department of Mathematics, Shahid Beheshti University, Tehran, Iran + Department of mathematics, Faculty of engineering and natural sciences, Istinye university, Istanbul, Türkiye

4. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

We will study the notion of right distributive ringoids over a field which are neither rings, semi-rings, semi-hyperrings nor near-rings. Matrices over ringoids are defined, and new concepts such as top-row-determinate and down-row-determinate related to 2 ? 2 matrices over a ringoid are introduced. Moreover, we investigate the notions of the (strongly, (very-) weak) orthogonality of vectors over a ringoid. Beside, we discuss the notion of incident vectors and define the concept of ??K-sphere on a ringoid, where K is a field and investigate some of their properties. Finally, we show that in a commutative ringoid all of the vectors are strongly orthogonal.

Publisher

National Library of Serbia

Reference10 articles.

1. O. Borůvka, Foundations of the theory of groupoids and groups, John Wiley & Sons, New York, 1976.

2. R. H. Bruck, A survey of binary systems, Springer, New York, 1971.

3. J. S. Han, H. S. Kim and J. Neggers, Fibonacci sequences in groupoids, Adv. Differ. Equ., 2012, (2012), 19. (doi:10.1186/1687-1847- 2012-19)

4. I. H. Hwang, H. S. Kim and J. Neggers, Some implicativities for groupoids and BCK-algebras, Math. J., 7 (2019), 973-800.

5. H. S. Kim, J. Neggers and S. S. Ahn, On pre-commutative algebras, Math. J., 7 (2019), 336-342.